Hybrid EKF - Machine Learning Framework for SOC -SOH Estimation in Sodium ION Batteries

Reliable battery management in emerging sodium-ion systems depends heavily on how well internal states can be estimated, especially parameters such as state of charge (SOC) and state of health(SOH). While sodium -ion chemistry offers clear advantage’s in terms of material abundance and cost, its electrochemical behaviour introduces Unique’s challenges for conventional estimation techniques, including reduced voltage sensitivity over extended SOC regions and pronounced temperature-dependent resistance variations. In this work, a unified estimation strategy is developed by incorporating a physics -driven Extended Kalman Filter(EKF) for improved performance with a lightweight neural network designed to compensate for model inaccuracies .In this work, the EKF is applied using a three-RC equivalent circuit representation to follow the dynamic response of Hard Carbon Na-ion battery packs, and a neural network is included to further improve the estimation and utilizes internal filter signals -particularly the voltage innovation to learn residual error patterns arising from parameter drift, temperature mismatch and non linear electrochemical effects .In addition SOH evolution is modelled using an Arrhenius -based degradation formulation, supported by an innovation -driven correction mechanism that links long -term estimation trends with aging behaviour .The system is studied under different temperature levels and changing current condition, and its behaviour is also observed over a longer aging duration. Results indicate significant improvements in estimation accuracy compared to standalone EKF and purely data -driven methods ,while maintaining low computational complexity suitable for embedded battery management systems .